1. 1
A Computational Model of Computer Virus Propagation
Li-Chiou Chen
lichiou@andrew.cmu.edu
Department of Engineering and Public Policy
Center for the Computational Model of Social and Organizational Analysis
Carnegie Mellon University
Kathleen M. Carley
KathleenCarley@andrew.cmu.edu
Department of Social and Decision Sciences
Center for the Computational Analysis of Social and Organizational Systems
H.J. Heinz III School of Public Policy and Management
Carnegie Mellon University
Extended Abstract
Computer virus infection is the most common computer security problem. This problem
has imposed significant amount of financial losses to organizations (CSI, 2000). Even
though most organizations have installed anti-virus software in their computers, majority of
them still experienced computer virus infection (ICSA, 2000). Most anti-virus software
could not detect a new virus unless it is patched with the new virus definition file.
Disseminating the new virus information and patches is hence important to raise user
awareness. However, little research has focused on evaluating the effectiveness of
disseminating new virus information on reducing virus infection. We hence propose a
corporate response model to investigate the effectiveness of warning message propagation.
In addition, we use the model to study the influence of social network topology on the virus
and warning message propagation.
A computer virus is a segment of program code that will copy its code into one or more
larger “host” programs when it is activated. A worm is a program that can run

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independently and travel from machine to machine across network connections (Spafford,
1990). We will refer computer viruses to both computers viruses and worms in Spafford’s
definition since most viruses today can be propagated in both ways.
Epidemic propagation models (Bailey, 1975) have been applied on modeling the
propagation of computer viruses (Kephart and White, 1993). Simulation models have been
used to discuss the influence of the network topology (Kephart, 1994)(Wang, 2000)(Pastor-
Satorras, 2001). However, neither the empirical topology data has been collected nor the
characteristics of the topology have been further studied. In addition, the warning message
propagation is related to the network topology, which could be a different network from the
virus propagation network.
A corporate response model is developed to describe computer viruses propagation and the
warning messages propagation. The components of the model include the inter-
organizational social network topology, the computer network topology, the virus
propagation mechanism, and the node state transition diagram. The four components are
described as follows:
1) The inter-organizational social network topology and computer network topology
are both represented as a graph G = (V, E, W(i,j)) where V is a set of nodes and E is
a set of edges. W(i,j) denotes the link between node i and j where i, j ∈ V. W(i,j) =
1 if a link exists between node i and node j and W(i,j) = 0 otherwise. We then apply
social network analysis (Wasserman, 1994) measures, such as density and
centralization, to characterize the network topology in our virtual experiments. A
new measure, isolation, is needed to describe the computer virus propagation
topology since the isolation nodes are critical to in the propagation process.
Isolation of graph G,
||
||
)(
V
S
GI = , is defined as the number of isolated nodes
divided by the total number of nodes in the graph. Isolated nodes refer to the nodes

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that do no have any links with other nodes in the same graph. S , = { i: ∀j∈V,
0),(
1
=∑=
N
j
jiW }, denotes a set of isolated nodes.
2) The virus propagation mechanisms are categorized as one-to-one, one-to-many,
many-to-one, and many-to-many. The category refers to the number of infection
source and the number of infection targets at once.
3) The node state transition diagram is used to describe the dynamics of a node over
time, such as if a node is infected by a virus or warned by a warning message. The
change of states is determined by the propagation of viruses through the social
network and the propagation of warning messages through the computer network.
We assume that the nodes will receive an automatic warning message if their
computers physically connect to a computer that has already had one.
Virtual experiments are conducted by varying the type of topology, the number of nodes,
density and isolation. Experiment results show that random graph topology generated by
the same density and isolation as real world data set could be used on modeling the social
network of computer virus propagation.
In addition, isolation is not an effective strategy for an organization if warning messages
are propagated in the network. Isolating an organization from other nodes in the social
network could isolate the node from virus infection but isolate the node from the warning
messages as well. This result contradicts with many organizations have assumed.
Bailey, N.J.T. 1975. The Mathematical Theory of Infectious Diseases and Its Applications.
New York: Oxford University Press.
CSI 2000. 'CSI/FBI Computer Crime and Security Survey' Computer Security Issues &
Trend.
ICSA 2000. 'ICSA Labs 6th Annual Computer Virus Prevalence Survey 2000': ICSA.net.
Kephart, J.O. and White, S.R. 1993. 'Measuring and Modeling Computer Virus Prevalence'
IEEE Computer Security Symposium on research in Security and Privacy. Oakland,
California.

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Kephart, J.O. 1994. 'How Topology Affects Population Dynamics' in Langton, C.G. (ed.)
Artificial Life III. Reading, MA: Addison-Wesley.
Pastor-Satorras, R. and Vespignani, A. 2001. 'Epidemic Dynamics and Endemic States in
Complex Networks' . Barcelona, Spain: Universitat Politecnica de Catalunya.
Spafford, E.H. 1994. 'Computer Viruses as Artificial Life'. Journal of Artificial Life.
Wang, C., Knight, J.C. and Elder, M.C. 2000. 'On Computer Viral Infection and the Effect
of Immunization' IEEE 16th Annual Computer Security Applications Conference.
Wasserman, S. and Faust, K. 1994. Social Network Analysis: Methods and Applications.
Cambridge: Cambridge University Press.